A Well-Tempered Hybrid Method for Solving Challenging Time-Dependent Density Functional Theory (TDDFT) Systems

The time-dependent Hartree–Fock (TDHF) and time-dependent density functional theory (TDDFT) equations allow one to probe electronic resonances of a system quickly and inexpensively. However, the iterative solution of the eigenvalue problem can be challenging or impossible to converge, using standard...

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Bibliographic Details
Published in:Journal of chemical theory and computation 2018-04, Vol.14 (4), p.2034-2041
Main Authors: Kasper, Joseph M, Williams-Young, David B, Vecharynski, Eugene, Yang, Chao, Li, Xiaosong
Format: Article
Language:English
Subjects:
Algorithms
Convergence
Density functional theory
Iterative methods
Iterative solution
Solvers
Time dependence
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Summary:The time-dependent Hartree–Fock (TDHF) and time-dependent density functional theory (TDDFT) equations allow one to probe electronic resonances of a system quickly and inexpensively. However, the iterative solution of the eigenvalue problem can be challenging or impossible to converge, using standard methods such as the Davidson algorithm for spectrally dense regions in the interior of the spectrum, as are common in X-ray absorption spectroscopy (XAS). More robust solvers, such as the generalized preconditioned locally harmonic residual (GPLHR) method, can alleviate this problem, but at the expense of higher average computational cost. A hybrid method is proposed which adapts to the problem in order to maximize computational performance while providing the superior convergence of GPLHR. In addition, a modification to the GPLHR algorithm is proposed to adaptively choose the shift parameter to enforce a convergence of states above a predefined energy threshold.
ISSN:1549-9618
1549-9626
DOI:10.1021/acs.jctc.8b00141